Negative resistance



' Nov. 9 192s.

1,606,350 M. M. DQLMAGE NEGATIVE RESISTANCE Filed Jvan. 24. 1922 AAIAAAAAAA 1.55. AAAAAAA Patented Nov. 9, 1926.

UNITED STATES PATENT orrics.

MIHRAN M. DOLMAGE, F WASHINGTON, DISTRICT OF COLUMBIA.

' NEGATIVE RESISTANCE.

Application led January 24, 1922. Serial No. 531,516.

in that it my be made to vary between very widely different limiting values.

The novel features of my invention I have pointed out in particularity in my claims. The invention itself will be best understood both as to its construction and method of operation, together with further objects and advantages, by reference to the following description taken in connection with the figure of the drawings which indicates the general arrangement of apparatus and wiring required to carry out my invention.

In the drawing, forming part of these specifications the combination of apparatus connected to terminals 1 and '2 to the right ofl the drawings represents a negative resistance. Connected to the last mentioned terminals, by dotted lines, are terminals 17 and 18 of an alternating source 1 in series with resistance 19. This resistance 19 includes the internal resistance of the generator and such additional resistance in series as the service requirements lmight demand. As an illustration, this alternating current source may be working over a givenltransmission line, in which case resistance 19 would represent the sum of the internal resistance of the alternating current source 1, and of the resistance of the line. Across terminals 1 and 2 is connected primary winding 3n of transformer A through two parallel paths-a path through primary winding 5 of shunt transformer B in series with resistance 7, and a second path through resist-ance and secondary winding 14 of output transformer D of amplifier 16.

The secondary windings 4 and 6 of transformer A and B are connected in parallel to resistance 8 and primary winding 9 of input transformer of amplifier 16. The secondary winding of this same input transformer is connected to potentiometer 11.

. The potentiometer itself is connected to grid battery 19 and to the negative pole of filament battery 20. The plate circuit of this same amplifier 16 is closed through a suitable plate battery and primary winding 13 of an output transformer. The secondary winding 0f this transformer is connected to res1stance 15 and to the junction point of primary windings 3 ,and 5, as shown.

The system shown-on the drawing, wired as just described, consists broadly of a network in whicha given electromotive force (that of alternating current source 1) is amplified and reimpressed back upon this same network in such a direction as `to overcome the electromotive force originally impressed. The arrangement will be made clearer by the following description of the method of operation of thel system. Electromotive force E of alternator l forces a current through resistance 19 and winding B of transformer A. This current divides into two parts,-a part which flows through winding 5 of shunt transformer B, and a part which flows through resistance 15 and secondary winding 14 of output transformer of amplifier 16. The two secondary windings 4 and 6 are so connected as to force through resistance 8 and input transformer winding 9, currents in the same direction when alternator' 1 is transmitting; and currents of opposite direction when amplifier 16 is transmitting through secondary winding 14 and resistance 15.- This will be readily understood by reference to the drawing.'

When, therefore, the originally impressed electromotive force E is transmitting, the induced electromotive forces in the'secondary parallel windings 4 and 6 are in the same direction with reference to the load, viz, resistance 8 and primary winding 9 of input transformer C.

The electric current obtained in the manner just described, in the' primary winding of input transformer C produces 1n the sec ondary winding 10 of this same transformer an induced electromotive force which is impressed, through potentiometer 11 and battery 12, upon the grid-filament circuit of amplifier 16. The correspondingamplified electromotive force is impressed upon the primary winding of output transformer D. The corresponding secondary electromotive force in winding 14 forces a current through resistance 15, which in turn divides itself into two parts-'a partthrough transformer winding 3 and a part through transformer current source 1. The net result of the ar-A rangement is that the resistance of the network., or system connected to terminals 1 and 2 to the right of the drawing, is negative Since the current flowing through source 1, resistance 19 and transformer winding 3 is in actual phase opposition to the electromotive force of alternating current source 1. In order that the negative resistance thus obtained should be stable andA free from reactive influences or singing, it is sufficient that resistance 7 be so chosen in referenceto resistance 19 as to secure a condition wliere the amplified electromotive force acting through transformer winding 14 can force nou current through the input transformer winding 9 of the same amplifier. As an instance,if windings 3 and 5 are of equal number of turns and of equal impedance and the corresponding secondary windings 4 and 6 bear the same equality relations to each other, then resistance 7 should be chosen equal to resistance-19. In such a case the currents, dueto the am-v pliied electromotive force acting through winding 14, flowing through windings 3 and 5 .will be necessarily equal to each other and, as the induced electromotive forces due to the two currents just mentioned are in hase opposition, no current will iow in lnput transformer winding 9. The system thus built is therefore entirely free from singing tendencies and is otherwise absolutely stable. The great ease with which the value of the negative resistance ma be adjusted will be clear if it'is realized t at an adjustment of the potentiometer will result in a change in the value of this negative resist ance without it being necessary to ymake any other changes in the network. The wide range of adjustment possible with the system described in these specifications will also be clearv if it is realized that, by a proper shifting of the potentiometer, the amplified electromotive force may be so reduced that there will be no current flow whatever through source 1 or winding 3. In such a case the'negative resistance has obviously a value equal to infinity. A further increase in the value of the amplification, obtained through amplifier 16, will result in a reductionof the value of the negative re` sistance.

The choice of the various constants of the circuit may be derived by the following mathematical analysis:

Let us call VzElectromotive force of an alternating current generator, having no internal impedance, connected directly to terminals 1 and 2 of the negative resistance as shown on Figure 1 of these specifications.

1L-Current through resistance 15 and sec.

ondary winding 14.

z'zzCurrent through shunt transformer winding 5 and element 7.

Ar-.Series resistance of gridcircuit of amplifier 16 as measured through primary winding 9 and of resistance 8.

B=Series resistance of plate circuit, as measured through secondary Winding 14, and of element 15. r

YzResistance of element 7.

YlzResistance of element 19.

'nlzRatio of turns of winding 10 to winding- 9.

azz-:Ratio of turns of winding 13 to Winding 14.

'nzRatio of turns of winding 5 to winding 6.

ILL-Resistance of grid circuit as measured through winding 9.

Raz-Resistance of element 15.

c=Coeicient` of a value less than or equal to unity depending upon the position of the potentiometer.

In order to simplify the analysis, we will assume that'windings 3 and 4 have unity ratio'of turns, Aand further that secondary windings 4 and 6 have the same impedance. Under these conditions the equations of the electric circuit are as follows It must be evident that the current flowing z'1+(nl}`1)z'2. Hence the electromotive force Athrough secondary winding 4 is equal to (i1-H12) and the current flowing through 110 winding 6, equal to (m12). Therefore the current through elements 9 and 10 must equal the sum of the above two currents or This electromotive force is multiplied by n, (ratio of turns of secondary winding 10. to

primary Winding 9), again multiplied by c Introducing vthe value of V', determined (a coefficient less than unity depending for as explained, into equation (1 and, as a 10 its numerical value upon the position of the matter of convenience, rearranging equapotentiometer), then again multiplied by p. tions (l) and (2) in function of z', and (which is the amplification constant of the +1).

vacuum tube) and is divided by n2. The 21+ n z2 value thus finally obtained is that of V of insteadof l and 2, We obtain-d 15 equation (3) above.

. Y Y (5) V= [A0/L+ l) -lhlj [al -I- (11+ Dbl-m @l In What follows We will represent by (a). Solving equations (4S) and (5), We obtain What We particularly Wish to obtain is the value of (il-|42). It is-given by:

We readily see from the above that the totall equivalent'rv resistance of the circuit, as given by To obtain further simplification weA will shoW the following values for A and B in function of a single quantity Y0, as fol1oWs:--A

nm -l- 1) where Yo is a resistance.

Substituting,- the Value of A and vB given above into equation (10), We` obtain:-

The resistance of the arrangement described in these specifications, as given by is in excess of (n+1) (Y-I-Yo), then the denominator is negative and the resistance of our circuit, as measured between terminals 1 and 2, will also become negative.

The system describednnder these specifications is absolutely stable and free from singing tendencies if used in an electrical network of constant resistance or impedance. It is sufficient, in order to obtain this condition, that the resistanceof the outside circuit connected to terminals 17 and 18, as measured from terminals 1 and 2, equal in value resistance 7 divided by (n). In such a case resistance 8 and input transformer Winding 9 are connected to points of the same potential and therefore no alternating current iiows through the grid-filament circuit of amplier 16, and hence there can be no singing tendency established. This point is evident where (n) equals 1. Where (n) is diii'erent from 1, the singing equa-A tion 18 shows that if Y equals WYI, the amplification of bulb 16 may have a value equal to without producing any reactive tendencies in the network.

The negative resistance forming the object of the present disclosure is not, however, limited in its use to conditions of constant outside impedance. It may be used with varying outsidev impedance conditions provided such variation is kept within certain limits.

Referring again to the drawing and using` the notation already established, assume that apotential (QJ) is established across transformer winding 9 for a short period of'time. This potential is increased (nl) times, multiplied ,als times and divided by (11,2), as`

already explained in detail. The plate potential of amplifier 16 is therefore equal to If we make, as before- Referring to the abovev equations relating to il and i2, we see that with the` relation BznA, the value of z', and 2 may be immediately'deduced as follows The current through transformer winding 9v is equalto (nig-i1), hence it is equal to Mursia)- The potential (fv) across winding 9, thus established, is equal to If RFA, thanl n+1 (Ya-Y0) (nYl-I-Yo) If ('v) is smaller than (fv), then the system cannot sing, hence the necessary condition to obtain stability is given byu Y0 @Y1-Y Xml-Kwart 1 which means that the constant (a) must not exceed- (Y+Yo) ('/LYl-FYO) (nYl-Y) (n+1) X Yo If the resistance Y1 of the outside circuit, instead of being constant and equal to Xn:

is variable, we may assume nYlzpY where (p) 1s some numeric 1n excess of unity. Then 1 If we establish a relation between (a), the maximum amplification possible with the amplifier installation available, and (YIYQ) and (n-l-l) as follows :4-

Negative resistance Negative resistance Then the above inequality may bey written as follows @Y -l- Yo p 1 which leads to the simple relation It is therefore clearrthat within extremely wide limits We may choose T20 so that it will naoYo- (n+1) (Y -I-Yo) Negative resistance Y0 2 -I- 1 ('17) Negative resistance in view of formula (15).

The minimum value of the negative resistance may also be expressed, provided (p) is in excess of 2, by the formula Negative resistance p-r in view of formula (16).

It will be noted that the value of-the negative resistance network, as given by formula (13), is independent of the degree of balance or lack of balance between element 19 and element 7 of the drawing. In the derivation of the fundamental equations no defi. nite numerical relationship was assumed between these two elements and these equations hold regardless of the relation between these elements, provided the unbalance is not such as to cause singing The special network described under these specifications is a negative resistance independent of frequency, since its value is given by formula (15) in which both Y and Y0 are ure resistanoes. It ma therefore be used or high as well as low requencies. It may be adjusted within extremely wide limits-'- between infinity and p- Another very important characteristic of the combination described, hereinabove is that it provldes a stable, non-oscillating negative resistance. It

. 1'n ohms of negative resistance produced by the apparatus. This negative resistance will stay fixed in value so long as the amplifying power of the amplifying bulb (13) is maintained constant.

The uses to which a negative resistance, as hereinbefore specified, may be put are so many that no attempt will be made to give a complete list of such uses. A most important applicationconsists in its use in the main antenna circuit of a radio receiving system, greatly increasing thereby the total amplification without bringingin any additional tendency to sing, Essentially the arrangement described is a bridge a'nd therefore complete freedom from singing may be obtained provided element 7 matches clement-19. It is also possible to reverse the wiring between elements and 7 on one hand and elements and 14 on the other hand and secure a new range of negative resistances.

1. An electrical network, -means to connect'said network to an outsidecircuit, an amplifier in said network, means to impress the output electromotive force of said amplifier uponvthe outside circuit in opposition of phase to the initial flow of current from said outside circuit to said network.

2.' An electrical network, means to connect said network to an outside circuit, an amplifier in said network, means to prevent the singing of said amplifier, means to `impress the output eleetromotive force of said amplifier upon the outside circuitl in opposition of phase to the initial flow of current from said outside circuit to said network.

3. An electrical network, means to connect said network to an outside circuit, an amplifier in said network, means to vary the output electromotive force of said amplifier and to impress said electromotive force upon the outside circuit in opposition of phase to the initial flow of current from said outside circuit to said network.

4. An electrical network, means to connect said network to an outside circuit, an amplifier in said network, means to prevent the singing of said amplifier, means to vary the output eleetromotive force of said amplifier and to impress said electromotive force'upon the outside circuit in opposition of phase to the initial flow of current from said outside circuit to said network.

5. An electrical network having a negative resistance independent of frequency,

f means to connect said network to an outside circuit, an amplifier in said network, means to impress the output electromotive force of said amplifier upon the outside circuit in opposition of phase to the initial flow of current from said outside circuit to .said network.

6. An electrical network having a negative resistance independent of frequency, means to connect said network to an outside circuit, an amplifier in said network, means to prevent the singing of sald amplifier, means to lmpress the output electromotive force of said amplifier upon the outside cir- 4;

cuit in opposition of phase to the initial flow of current from said outside circuit 'to saidl network.

7. An electrical network having a negative resistance independent of frequency, means 5 to connect said network to an outside circuit, an amplifier in said network, means to vary the output electromotivc force of said amplifier and to impress said electron'xotivc force upon the outside circuit in opposition 5 of phase to the initial flow of current from said outside circuit to said network.

8. An velectrical network having a negative resistance independent of frequency, means to connect said network to an outside 6 circuit, an amplifier in said network, means to prevent the singing of said amplifier, means to vary the output electromotive force of said amplifier and to impress said electromotive force upon the out-side circuit in op- 6 position of phase `to the initial fiow of cur rent from said outside circuit to said network.

9. In combination1 a bridge circuit containing an amplifying system with its initial input and final output circuits occupying opposite arms, an outside circuit and a balancing network also occupying opposite arms in said bridge, an electromotive force in said outside circuit and means to superimpose upon said outside circuit the electromotive force of the final output circuit of said amplifying system.

In testimony whereof I affix my signature.

MIHRAN M. DOLMAGE. 

